"Brian M. Scott" <b.scott@[EMAIL PROTECTED]
> wrote in message
news:hmapmaf61g2e$.1dk3xpc4s4kgu.dlg@[EMAIL PROTECTED]
> On Sat, 19 Jul 2008 19:58:13 +0100, Jack <jj@[EMAIL PROTECTED]
>
> wrote in <news:8Pqgk.9112$X72.6423@[EMAIL PROTECTED]
> in
> alt.algebra.help:
>
>>>> Well how would I do it then? I have defined p and q as
>>>> members of J and now I want to say that I want to
>>>> consider the case where B is dependent upon all possible
>>>> p and q.
>
>> Every possible member of J can be considered a prime p,
>> and, also, every possible member of J can be considered
>> a prime q; the sole criterion -- if it's worth anything,
>> what with all the members ultimately being both a p and
>> a q -- is that when considering one member as p, a
>> different one is considered to be q.
>
> In English: p and q always represent distinct members of J.
>
>>> First you'll have to explain what you mean by this.
>>> Precisely HOW is the set to depend on all of the members of
>>> J? Under exactly what conditions does an integer b get to
>>> belong to the set that you want to call B(x, J)?
>
>> The integer b is a member of B if and only if any p or q
>> divide n in [x,y] such that n=(y+1)/2-b, or n=
>> (y+1)/2+b.
>
> This is incomprehensible.
Why? It's exactly as you had it: B(x, p, q) = {b \in |N : p | x + b or q |
x - b}.
If I might do my best to give a tantalising insight into my gobbledegook
world, this is the way I formulated - for what it's worth - what I wrote:
We take only ('such that') those 'n' for which ('n=...') if you subtract b
from (y+1)/2 ('....=(y+1)/2-b') and get p,q|n ('if any p or q divide n')
then you get a member of B ('integer b is a member of B if and only
if...').
My only issues are how I convey to the reader that the members of B(x, p,
q)
are always integers n in [1,y]; and that x is always (1+y)/2; and that I
want to be able to refer to a set in which every possible p and q, i.e.
every member of J, is considered in such a fa****on.
On the last of those, I've been thinking of making a reference to J_{p,q)
(instead of to p,q, so it is B(x,J_{pq})) for the case in which I am only
considering two members of J; and simply J when I am considering all of
them. But I am concerned that the reference simply to J will be
insufficient
to indicate what I am intending.
Cheers.
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